Q. f(x)=ln (12x-5/9x-2)
So by using the chain rule, i can get:
(-4/3)((9x-2)2/(12x-5)2)
and by using the quotient rule, i can get the final answer, which is:
(2(-36x-8)(-36x-15)2-2(-36x-15)(-36x-8)2)
------------------------------------------------------------------...
y = sin( 4 x ) cos( 3 x )
f(x) = sin4x
g(x) = cos3x
f'(x) = cos4x
g'(x) = -sin3x
And by using the product rule, i'll get:
cos4x(cos3x) - sin4x(sin3x)
Is the answer correct or can be simplify again??
y = ( 5 x-2 ) 3 / ( 2 x+5 ) 4
I do it this way:
f(x) = (5x-2)3
g(x) = (2x+5)-4
f'(x) = 3(5x-2)2
g'(x) = -4(2x+5)-5
By using the product rule:
[3(5x-2)2](2x+5)-4 + (5x-2)3[-4(2x+5)-5]
3(5x-2)2(2x+5)-4 -4(2x+5)-5(5x-2)3
What's wrong with this answer?